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Minimally almost periodic totally disconnected groups
Author(s):
Claudio
Nebbia
Journal:
Proc. Amer. Math. Soc.
128
(2000),
347-351.
MSC (1991):
Primary 20E08;
Secondary 22D05, 43A60
Posted:
June 21, 1999
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Abstract:
In this paper we prove that every closed noncompact group of isometries of a homogeneous tree which acts transitively on the tree boundary contains a normal closed cocompact subgroup which is minimally almost periodic. Moreover we prove that is a topologically simple group.
References:
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-algèbres et leurs représentation, Gauthier-Villars, Paris, 1969. MR 98a:46066 - 2.
- A. Figà-Talamanca and C. Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees, London Math. Soc. Lecture Note Series, 162, Cambridge University Press, 1991. MR 93f:22004
- 3.
- H. Jacquet and R. P. Langlands, Automorphic forms on
, Lecture Notes in Math., 114, Springer-Verlag, 1970. MR 53:5481 - 4.
- C. Nebbia, Groups of isometries of a tree and the Kunze-Stein phenomenon, Pacific J. Math. 133 (1) (1988), 141-149. MR 89h:43005
- 5.
- C. Nebbia, Classification of all irreducible unitary representations of the stabilizer of the horocycles of a tree, Israel J. Math. 70 (3) (1990), 343-351. MR 91m:22009
- 6.
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shianskii, Classification of all irreducible representations of groups of automorphisms of Bruhat-Tits trees, Functional Anal. Appl. 11 (1977), 26-34. - 7.
- J. P. Serre, Arbres, amalgames,
, Astérisque, 46, 1977. MR 57:16426 - 8.
- J. Tits, Sur le groupe des automorphismes d'un arbre, Essays on topology and related topics, Mémoires dédiés à G. de Rham, Springer-Verlag, Berlin 1970, 188-211. MR 45:8582
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Additional Information:
Claudio
Nebbia
Affiliation:
Dipartimento di Matematica ``G. Castelnuovo'', Università di Roma ``La Sapienza'', 00185 Roma, Italy
Email:
nebbia@mercurio.mat.uniroma1.it
DOI:
10.1090/S0002-9939-99-05027-3
PII:
S 0002-9939(99)05027-3
Received by editor(s):
November 20, 1997
Received by editor(s) in revised form:
March 31, 1998
Posted:
June 21, 1999
Communicated by:
Roe Goodman
Copyright of article:
Copyright
1999,
American Mathematical Society
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